Question: Solve for $x$ : $4\sqrt{x} - 4 = 7\sqrt{x} + 3$
Solution: Subtract $4\sqrt{x}$ from both sides: $(4\sqrt{x} - 4) - 4\sqrt{x} = (7\sqrt{x} + 3) - 4\sqrt{x}$ $-4 = 3\sqrt{x} + 3$ Subtract $3$ from both sides: $-4 - 3 = (3\sqrt{x} + 3) - 3$ $-7 = 3\sqrt{x}$ Divide both sides by $3$ $\frac{-7}{3} = \frac{3\sqrt{x}}{3}$ Simplify. $-\dfrac{7}{3} = \sqrt{x}$ The principal root of a number cannot be negative. So, there is no solution.